HW4
William Chance, Shray Mittal, Benjamin Leu
November 6, 2019
1)
1a)
The two trends seem to be correlated. With more searches for over the counter medicine, we observe higher reported incidents of the flu.
1b)
## Loading required package: lattice## Loading required package: ggplot2##
## Call:
## lm(formula = .outcome ~ ., data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1125.38 -215.48 -57.62 200.12 1808.87
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 524.97 36.16 14.517 < 2e-16 ***
## flu.and.fever 232.42 50.01 4.648 6.41e-06 ***
## treat.a.fever 331.66 46.52 7.130 2.25e-11 ***
## over.the.counter.flu.medicine 166.83 49.79 3.351 0.000979 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 407.2 on 183 degrees of freedom
## Multiple R-squared: 0.748, Adjusted R-squared: 0.7439
## F-statistic: 181.1 on 3 and 183 DF, p-value: < 2.2e-16
##
## Call:
## lm(formula = .outcome ~ ., data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -727.06 -118.84 13.34 107.51 746.73
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 650.070 102.724 6.328
## dangerous.fever 6.624 44.611 0.148
## how.long.does.flu.last 112.522 113.565 0.991
## i.have.the.flu 47.143 155.974 0.302
## fever.cough 26.160 114.876 0.228
## what.to.eat.when.you.have.the.flu 78.434 90.993 0.862
## medicine.for.flu 73.702 96.988 0.760
## how.long.are.you.contagious.with.the.flu 60.534 94.375 0.641
## viral.pneumonia 131.972 108.066 1.221
## how.to.get.over.the.flu 109.290 88.471 1.235
## treat.the.flu -4.365 143.158 -0.030
## signs.of.the.flu 105.139 136.883 0.768
## flu.contagious -28.723 47.785 -0.601
## ear.thermometer -24.540 46.422 -0.529
## can.dogs.get.the.flu 49.540 88.345 0.561
## anas.barbariae.hepatis 180.924 171.809 1.053
## how.to.treat.flu 54.896 80.958 0.678
## cure.flu 240.281 87.556 2.744
## treat.flu 48.808 61.494 0.794
## cold.or.flu 5.412 78.110 0.069
## what.is.a.high.fever 45.964 89.651 0.513
## oscillococcinum 6.993 41.147 0.170
## treatment.for.flu 118.225 95.295 1.241
## remedies.for.flu -469.385 170.594 -2.751
## how.to.get.rid.of.the.flu 70.409 47.655 1.477
## bacterial.pneumonia -9.192 44.981 -0.204
## symptoms.of.the.flu -146.627 78.035 -1.879
## fever.and.cough -42.277 39.903 -1.060
## braun.thermoscan -30.003 43.484 -0.690
## how.long.am.i.contagious -35.290 100.262 -0.352
## home.remedies.for.flu 75.810 118.393 0.640
## cough.fever -75.190 105.393 -0.713
## cure.the.flu -108.147 100.334 -1.078
## low.body.temperature -164.870 75.767 -2.176
## contagious.flu 74.350 92.466 0.804
## headache.cough 34.856 76.553 0.455
## painful.cough 112.676 88.771 1.269
## get.rid.of.flu 17.503 70.517 0.248
## normal.body -13.401 60.376 -0.222
## cough.headache -19.956 47.638 -0.419
## how.to.fight.the.flu -27.925 71.412 -0.391
## flu.or.cold -224.979 131.513 -1.711
## over.the.counter.flu.medicine -11.040 75.777 -0.146
## flu.and.fever -23.602 63.105 -0.374
## viral.bronchitis -9.749 35.840 -0.272
## thermoscan 35.770 39.797 0.899
## taking.temperature 77.330 46.126 1.676
## influenza.a.and.b 53.689 82.896 0.648
## fever.flu 148.622 121.825 1.220
## oral.thermometer 84.065 75.072 1.120
## the.flu -3.288 26.280 -0.125
## medicine.for.the.flu 38.271 84.036 0.455
## treat.a.fever -83.540 89.522 -0.933
## cough.after.flu -5.898 59.443 -0.099
## acute.bronchitis 48.616 59.122 0.822
## what.to.do.when.you.have.the.flu -46.138 56.425 -0.818
## bronchitis 43.948 68.188 0.645
## extractum -5.358 48.973 -0.109
## best.flu.medicine 13.035 82.488 0.158
## how.long.are.you.contagious -31.320 61.337 -0.511
## fever.reducers 137.137 67.429 2.034
## body.temperature 5.797 45.418 0.128
## reduce.fever -80.360 51.489 -1.561
## flu.remedies -266.712 165.695 -1.610
## anas.barbariae.hepatis.et.cordis -33.038 119.397 -0.277
## remedies.for.the.flu -4.339 104.555 -0.041
## symptoms.pneumonia -36.741 36.220 -1.014
## viral.syndrome 18.963 85.238 0.222
## the.flu.symptoms -8.364 76.729 -0.109
## what.is.influenza 35.666 96.191 0.371
## pneumonia 61.522 48.644 1.265
## fever.temperature 9.903 30.724 0.322
## child.temperature 23.695 67.496 0.351
## incubation.period.for.the.flu -84.795 76.596 -1.107
## high.fever -69.326 63.816 -1.086
## low.body.temp 21.658 39.453 0.549
## how.long.does.fever.last 117.271 83.844 1.399
## is.it.the.flu -17.397 56.482 -0.308
## what.to.do.for.the.flu 4.239 66.492 0.064
## fight.the.flu 148.720 143.110 1.039
## symptoms.of.bronchitis -11.811 123.205 -0.096
## bacterial.bronchitis 15.883 78.877 0.201
## chest.cough -63.952 59.469 -1.075
## fever.breaks -50.428 86.757 -0.581
## cough.and.fever 18.906 40.381 0.468
## fever.too.high 24.154 91.022 0.265
## early.flu.symptoms -48.954 93.830 -0.522
## Pr(>|t|)
## (Intercept) 7.06e-09 ***
## dangerous.fever 0.88225
## how.long.does.flu.last 0.32417
## i.have.the.flu 0.76309
## fever.cough 0.82032
## what.to.eat.when.you.have.the.flu 0.39076
## medicine.for.flu 0.44910
## how.long.are.you.contagious.with.the.flu 0.52272
## viral.pneumonia 0.22487
## how.to.get.over.the.flu 0.21960
## treat.the.flu 0.97574
## signs.of.the.flu 0.44424
## flu.contagious 0.54914
## ear.thermometer 0.59824
## can.dogs.get.the.flu 0.57622
## anas.barbariae.hepatis 0.29485
## how.to.treat.flu 0.49929
## cure.flu 0.00719 **
## treat.flu 0.42925
## cold.or.flu 0.94490
## what.is.a.high.fever 0.60929
## oscillococcinum 0.86540
## treatment.for.flu 0.21765
## remedies.for.flu 0.00704 **
## how.to.get.rid.of.the.flu 0.14269
## bacterial.pneumonia 0.83849
## symptoms.of.the.flu 0.06316 .
## fever.and.cough 0.29192
## braun.thermoscan 0.49181
## how.long.am.i.contagious 0.72560
## home.remedies.for.flu 0.52342
## cough.fever 0.47724
## cure.the.flu 0.28369
## low.body.temperature 0.03191 *
## contagious.flu 0.42326
## headache.cough 0.64987
## painful.cough 0.20729
## get.rid.of.flu 0.80448
## normal.body 0.82480
## cough.headache 0.67619
## how.to.fight.the.flu 0.69660
## flu.or.cold 0.09024 .
## over.the.counter.flu.medicine 0.88445
## flu.and.fever 0.70918
## viral.bronchitis 0.78616
## thermoscan 0.37091
## taking.temperature 0.09677 .
## influenza.a.and.b 0.51868
## fever.flu 0.22535
## oral.thermometer 0.26549
## the.flu 0.90069
## medicine.for.the.flu 0.64980
## treat.a.fever 0.35298
## cough.after.flu 0.92116
## acute.bronchitis 0.41286
## what.to.do.when.you.have.the.flu 0.41547
## bronchitis 0.52072
## extractum 0.91310
## best.flu.medicine 0.87476
## how.long.are.you.contagious 0.61074
## fever.reducers 0.04462 *
## body.temperature 0.89869
## reduce.fever 0.12175
## flu.remedies 0.11063
## anas.barbariae.hepatis.et.cordis 0.78258
## remedies.for.the.flu 0.96698
## symptoms.pneumonia 0.31284
## viral.syndrome 0.82440
## the.flu.symptoms 0.91341
## what.is.influenza 0.71159
## pneumonia 0.20890
## fever.temperature 0.74789
## child.temperature 0.72628
## incubation.period.for.the.flu 0.27093
## high.fever 0.27994
## low.body.temp 0.58427
## how.long.does.fever.last 0.16500
## is.it.the.flu 0.75871
## what.to.do.for.the.flu 0.94929
## fight.the.flu 0.30122
## symptoms.of.bronchitis 0.92382
## bacterial.bronchitis 0.84082
## chest.cough 0.28479
## fever.breaks 0.56238
## cough.and.fever 0.64067
## fever.too.high 0.79128
## early.flu.symptoms 0.60301
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 276.4 on 100 degrees of freedom
## Multiple R-squared: 0.9365, Adjusted R-squared: 0.882
## F-statistic: 17.16 on 86 and 100 DF, p-value: < 2.2e-16
## Start: AIC=1930.17
## .outcome ~ dangerous.fever + how.long.does.flu.last + i.have.the.flu +
## fever.cough + what.to.eat.when.you.have.the.flu + medicine.for.flu +
## how.long.are.you.contagious.with.the.flu + viral.pneumonia +
## how.to.get.over.the.flu + treat.the.flu + signs.of.the.flu +
## flu.contagious + ear.thermometer + can.dogs.get.the.flu +
## anas.barbariae.hepatis + how.to.treat.flu + cure.flu + treat.flu +
## cold.or.flu + what.is.a.high.fever + oscillococcinum + treatment.for.flu +
## remedies.for.flu + how.to.get.rid.of.the.flu + bacterial.pneumonia +
## symptoms.of.the.flu + fever.and.cough + braun.thermoscan +
## how.long.am.i.contagious + home.remedies.for.flu + cough.fever +
## cure.the.flu + low.body.temperature + contagious.flu + headache.cough +
## painful.cough + get.rid.of.flu + normal.body + cough.headache +
## how.to.fight.the.flu + flu.or.cold + over.the.counter.flu.medicine +
## flu.and.fever + viral.bronchitis + thermoscan + taking.temperature +
## influenza.a.and.b + fever.flu + oral.thermometer + the.flu +
## medicine.for.the.flu + treat.a.fever + cough.after.flu +
## acute.bronchitis + what.to.do.when.you.have.the.flu + bronchitis +
## extractum + best.flu.medicine + how.long.are.you.contagious +
## fever.reducers + body.temperature + reduce.fever + flu.remedies +
## anas.barbariae.hepatis.et.cordis + remedies.for.the.flu +
## symptoms.pneumonia + viral.syndrome + the.flu.symptoms +
## what.is.influenza + pneumonia + fever.temperature + child.temperature +
## incubation.period.for.the.flu + high.fever + low.body.temp +
## how.long.does.fever.last + is.it.the.flu + what.to.do.for.the.flu +
## fight.the.flu + symptoms.of.bronchitis + bacterial.bronchitis +
## chest.cough + fever.breaks + cough.and.fever + fever.too.high +
## early.flu.symptoms
##
## Start: AIC=1930.06
## .outcome ~ dangerous.fever + how.long.does.flu.last + i.have.the.flu +
## fever.cough + what.to.eat.when.you.have.the.flu + medicine.for.flu +
## how.long.are.you.contagious.with.the.flu + viral.pneumonia +
## how.to.get.over.the.flu + treat.the.flu + signs.of.the.flu +
## flu.contagious + ear.thermometer + can.dogs.get.the.flu +
## anas.barbariae.hepatis + how.to.treat.flu + cure.flu + treat.flu +
## cold.or.flu + what.is.a.high.fever + oscillococcinum + treatment.for.flu +
## remedies.for.flu + how.to.get.rid.of.the.flu + bacterial.pneumonia +
## symptoms.of.the.flu + fever.and.cough + braun.thermoscan +
## how.long.am.i.contagious + home.remedies.for.flu + cough.fever +
## cure.the.flu + low.body.temperature + contagious.flu + headache.cough +
## painful.cough + get.rid.of.flu + normal.body + cough.headache +
## how.to.fight.the.flu + flu.or.cold + over.the.counter.flu.medicine +
## flu.and.fever + viral.bronchitis + thermoscan + taking.temperature +
## influenza.a.and.b + fever.flu + oral.thermometer + the.flu +
## medicine.for.the.flu + treat.a.fever + cough.after.flu +
## acute.bronchitis + what.to.do.when.you.have.the.flu + bronchitis +
## extractum + best.flu.medicine + how.long.are.you.contagious +
## fever.reducers + body.temperature + reduce.fever + flu.remedies +
## anas.barbariae.hepatis.et.cordis + remedies.for.the.flu +
## symptoms.pneumonia + viral.syndrome + the.flu.symptoms +
## what.is.influenza + pneumonia + fever.temperature + child.temperature +
## incubation.period.for.the.flu + high.fever + low.body.temp +
## how.long.does.fever.last + is.it.the.flu + what.to.do.for.the.flu +
## fight.the.flu + symptoms.of.bronchitis + bacterial.bronchitis +
## chest.cough + fever.breaks + cough.and.fever + fever.too.high +
## early.flu.symptoms
##
## Start: AIC=1964.42
## .outcome ~ dangerous.fever + how.long.does.flu.last + i.have.the.flu +
## fever.cough + what.to.eat.when.you.have.the.flu + medicine.for.flu +
## how.long.are.you.contagious.with.the.flu + viral.pneumonia +
## how.to.get.over.the.flu + treat.the.flu + signs.of.the.flu +
## flu.contagious + ear.thermometer + can.dogs.get.the.flu +
## anas.barbariae.hepatis + how.to.treat.flu + cure.flu + treat.flu +
## cold.or.flu + what.is.a.high.fever + oscillococcinum + treatment.for.flu +
## remedies.for.flu + how.to.get.rid.of.the.flu + bacterial.pneumonia +
## symptoms.of.the.flu + fever.and.cough + braun.thermoscan +
## how.long.am.i.contagious + home.remedies.for.flu + cough.fever +
## cure.the.flu + low.body.temperature + contagious.flu + headache.cough +
## painful.cough + get.rid.of.flu + normal.body + cough.headache +
## how.to.fight.the.flu + flu.or.cold + over.the.counter.flu.medicine +
## flu.and.fever + viral.bronchitis + thermoscan + taking.temperature +
## influenza.a.and.b + fever.flu + oral.thermometer + the.flu +
## medicine.for.the.flu + treat.a.fever + cough.after.flu +
## acute.bronchitis + what.to.do.when.you.have.the.flu + bronchitis +
## extractum + best.flu.medicine + how.long.are.you.contagious +
## fever.reducers + body.temperature + reduce.fever + flu.remedies +
## anas.barbariae.hepatis.et.cordis + remedies.for.the.flu +
## symptoms.pneumonia + viral.syndrome + the.flu.symptoms +
## what.is.influenza + pneumonia + fever.temperature + child.temperature +
## incubation.period.for.the.flu + high.fever + low.body.temp +
## how.long.does.fever.last + is.it.the.flu + what.to.do.for.the.flu +
## fight.the.flu + symptoms.of.bronchitis + bacterial.bronchitis +
## chest.cough + fever.breaks + cough.and.fever + fever.too.high +
## early.flu.symptoms
##
## Start: AIC=1954.38
## .outcome ~ dangerous.fever + how.long.does.flu.last + i.have.the.flu +
## fever.cough + what.to.eat.when.you.have.the.flu + medicine.for.flu +
## how.long.are.you.contagious.with.the.flu + viral.pneumonia +
## how.to.get.over.the.flu + treat.the.flu + signs.of.the.flu +
## flu.contagious + ear.thermometer + can.dogs.get.the.flu +
## anas.barbariae.hepatis + how.to.treat.flu + cure.flu + treat.flu +
## cold.or.flu + what.is.a.high.fever + oscillococcinum + treatment.for.flu +
## remedies.for.flu + how.to.get.rid.of.the.flu + bacterial.pneumonia +
## symptoms.of.the.flu + fever.and.cough + braun.thermoscan +
## how.long.am.i.contagious + home.remedies.for.flu + cough.fever +
## cure.the.flu + low.body.temperature + contagious.flu + headache.cough +
## painful.cough + get.rid.of.flu + normal.body + cough.headache +
## how.to.fight.the.flu + flu.or.cold + over.the.counter.flu.medicine +
## flu.and.fever + viral.bronchitis + thermoscan + taking.temperature +
## influenza.a.and.b + fever.flu + oral.thermometer + the.flu +
## medicine.for.the.flu + treat.a.fever + cough.after.flu +
## acute.bronchitis + what.to.do.when.you.have.the.flu + bronchitis +
## extractum + best.flu.medicine + how.long.are.you.contagious +
## fever.reducers + body.temperature + reduce.fever + flu.remedies +
## anas.barbariae.hepatis.et.cordis + remedies.for.the.flu +
## symptoms.pneumonia + viral.syndrome + the.flu.symptoms +
## what.is.influenza + pneumonia + fever.temperature + child.temperature +
## incubation.period.for.the.flu + high.fever + low.body.temp +
## how.long.does.fever.last + is.it.the.flu + what.to.do.for.the.flu +
## fight.the.flu + symptoms.of.bronchitis + bacterial.bronchitis +
## chest.cough + fever.breaks + cough.and.fever + fever.too.high +
## early.flu.symptoms
##
## Start: AIC=1919.27
## .outcome ~ dangerous.fever + how.long.does.flu.last + i.have.the.flu +
## fever.cough + what.to.eat.when.you.have.the.flu + medicine.for.flu +
## how.long.are.you.contagious.with.the.flu + viral.pneumonia +
## how.to.get.over.the.flu + treat.the.flu + signs.of.the.flu +
## flu.contagious + ear.thermometer + can.dogs.get.the.flu +
## anas.barbariae.hepatis + how.to.treat.flu + cure.flu + treat.flu +
## cold.or.flu + what.is.a.high.fever + oscillococcinum + treatment.for.flu +
## remedies.for.flu + how.to.get.rid.of.the.flu + bacterial.pneumonia +
## symptoms.of.the.flu + fever.and.cough + braun.thermoscan +
## how.long.am.i.contagious + home.remedies.for.flu + cough.fever +
## cure.the.flu + low.body.temperature + contagious.flu + headache.cough +
## painful.cough + get.rid.of.flu + normal.body + cough.headache +
## how.to.fight.the.flu + flu.or.cold + over.the.counter.flu.medicine +
## flu.and.fever + viral.bronchitis + thermoscan + taking.temperature +
## influenza.a.and.b + fever.flu + oral.thermometer + the.flu +
## medicine.for.the.flu + treat.a.fever + cough.after.flu +
## acute.bronchitis + what.to.do.when.you.have.the.flu + bronchitis +
## extractum + best.flu.medicine + how.long.are.you.contagious +
## fever.reducers + body.temperature + reduce.fever + flu.remedies +
## anas.barbariae.hepatis.et.cordis + remedies.for.the.flu +
## symptoms.pneumonia + viral.syndrome + the.flu.symptoms +
## what.is.influenza + pneumonia + fever.temperature + child.temperature +
## incubation.period.for.the.flu + high.fever + low.body.temp +
## how.long.does.fever.last + is.it.the.flu + what.to.do.for.the.flu +
## fight.the.flu + symptoms.of.bronchitis + bacterial.bronchitis +
## chest.cough + fever.breaks + cough.and.fever + fever.too.high +
## early.flu.symptoms
##
## Start: AIC=1949.92
## .outcome ~ dangerous.fever + how.long.does.flu.last + i.have.the.flu +
## fever.cough + what.to.eat.when.you.have.the.flu + medicine.for.flu +
## how.long.are.you.contagious.with.the.flu + viral.pneumonia +
## how.to.get.over.the.flu + treat.the.flu + signs.of.the.flu +
## flu.contagious + ear.thermometer + can.dogs.get.the.flu +
## anas.barbariae.hepatis + how.to.treat.flu + cure.flu + treat.flu +
## cold.or.flu + what.is.a.high.fever + oscillococcinum + treatment.for.flu +
## remedies.for.flu + how.to.get.rid.of.the.flu + bacterial.pneumonia +
## symptoms.of.the.flu + fever.and.cough + braun.thermoscan +
## how.long.am.i.contagious + home.remedies.for.flu + cough.fever +
## cure.the.flu + low.body.temperature + contagious.flu + headache.cough +
## painful.cough + get.rid.of.flu + normal.body + cough.headache +
## how.to.fight.the.flu + flu.or.cold + over.the.counter.flu.medicine +
## flu.and.fever + viral.bronchitis + thermoscan + taking.temperature +
## influenza.a.and.b + fever.flu + oral.thermometer + the.flu +
## medicine.for.the.flu + treat.a.fever + cough.after.flu +
## acute.bronchitis + what.to.do.when.you.have.the.flu + bronchitis +
## extractum + best.flu.medicine + how.long.are.you.contagious +
## fever.reducers + body.temperature + reduce.fever + flu.remedies +
## anas.barbariae.hepatis.et.cordis + remedies.for.the.flu +
## symptoms.pneumonia + viral.syndrome + the.flu.symptoms +
## what.is.influenza + pneumonia + fever.temperature + child.temperature +
## incubation.period.for.the.flu + high.fever + low.body.temp +
## how.long.does.fever.last + is.it.the.flu + what.to.do.for.the.flu +
## fight.the.flu + symptoms.of.bronchitis + bacterial.bronchitis +
## chest.cough + fever.breaks + cough.and.fever + fever.too.high +
## early.flu.symptoms
##
## Start: AIC=1872.37
## .outcome ~ dangerous.fever + how.long.does.flu.last + i.have.the.flu +
## fever.cough + what.to.eat.when.you.have.the.flu + medicine.for.flu +
## how.long.are.you.contagious.with.the.flu + viral.pneumonia +
## how.to.get.over.the.flu + treat.the.flu + signs.of.the.flu +
## flu.contagious + ear.thermometer + can.dogs.get.the.flu +
## anas.barbariae.hepatis + how.to.treat.flu + cure.flu + treat.flu +
## cold.or.flu + what.is.a.high.fever + oscillococcinum + treatment.for.flu +
## remedies.for.flu + how.to.get.rid.of.the.flu + bacterial.pneumonia +
## symptoms.of.the.flu + fever.and.cough + braun.thermoscan +
## how.long.am.i.contagious + home.remedies.for.flu + cough.fever +
## cure.the.flu + low.body.temperature + contagious.flu + headache.cough +
## painful.cough + get.rid.of.flu + normal.body + cough.headache +
## how.to.fight.the.flu + flu.or.cold + over.the.counter.flu.medicine +
## flu.and.fever + viral.bronchitis + thermoscan + taking.temperature +
## influenza.a.and.b + fever.flu + oral.thermometer + the.flu +
## medicine.for.the.flu + treat.a.fever + cough.after.flu +
## acute.bronchitis + what.to.do.when.you.have.the.flu + bronchitis +
## extractum + best.flu.medicine + how.long.are.you.contagious +
## fever.reducers + body.temperature + reduce.fever + flu.remedies +
## anas.barbariae.hepatis.et.cordis + remedies.for.the.flu +
## symptoms.pneumonia + viral.syndrome + the.flu.symptoms +
## what.is.influenza + pneumonia + fever.temperature + child.temperature +
## incubation.period.for.the.flu + high.fever + low.body.temp +
## how.long.does.fever.last + is.it.the.flu + what.to.do.for.the.flu +
## fight.the.flu + symptoms.of.bronchitis + bacterial.bronchitis +
## chest.cough + fever.breaks + cough.and.fever + fever.too.high +
## early.flu.symptoms
##
## Start: AIC=1952.2
## .outcome ~ dangerous.fever + how.long.does.flu.last + i.have.the.flu +
## fever.cough + what.to.eat.when.you.have.the.flu + medicine.for.flu +
## how.long.are.you.contagious.with.the.flu + viral.pneumonia +
## how.to.get.over.the.flu + treat.the.flu + signs.of.the.flu +
## flu.contagious + ear.thermometer + can.dogs.get.the.flu +
## anas.barbariae.hepatis + how.to.treat.flu + cure.flu + treat.flu +
## cold.or.flu + what.is.a.high.fever + oscillococcinum + treatment.for.flu +
## remedies.for.flu + how.to.get.rid.of.the.flu + bacterial.pneumonia +
## symptoms.of.the.flu + fever.and.cough + braun.thermoscan +
## how.long.am.i.contagious + home.remedies.for.flu + cough.fever +
## cure.the.flu + low.body.temperature + contagious.flu + headache.cough +
## painful.cough + get.rid.of.flu + normal.body + cough.headache +
## how.to.fight.the.flu + flu.or.cold + over.the.counter.flu.medicine +
## flu.and.fever + viral.bronchitis + thermoscan + taking.temperature +
## influenza.a.and.b + fever.flu + oral.thermometer + the.flu +
## medicine.for.the.flu + treat.a.fever + cough.after.flu +
## acute.bronchitis + what.to.do.when.you.have.the.flu + bronchitis +
## extractum + best.flu.medicine + how.long.are.you.contagious +
## fever.reducers + body.temperature + reduce.fever + flu.remedies +
## anas.barbariae.hepatis.et.cordis + remedies.for.the.flu +
## symptoms.pneumonia + viral.syndrome + the.flu.symptoms +
## what.is.influenza + pneumonia + fever.temperature + child.temperature +
## incubation.period.for.the.flu + high.fever + low.body.temp +
## how.long.does.fever.last + is.it.the.flu + what.to.do.for.the.flu +
## fight.the.flu + symptoms.of.bronchitis + bacterial.bronchitis +
## chest.cough + fever.breaks + cough.and.fever + fever.too.high +
## early.flu.symptoms
##
## Start: AIC=1925.5
## .outcome ~ dangerous.fever + how.long.does.flu.last + i.have.the.flu +
## fever.cough + what.to.eat.when.you.have.the.flu + medicine.for.flu +
## how.long.are.you.contagious.with.the.flu + viral.pneumonia +
## how.to.get.over.the.flu + treat.the.flu + signs.of.the.flu +
## flu.contagious + ear.thermometer + can.dogs.get.the.flu +
## anas.barbariae.hepatis + how.to.treat.flu + cure.flu + treat.flu +
## cold.or.flu + what.is.a.high.fever + oscillococcinum + treatment.for.flu +
## remedies.for.flu + how.to.get.rid.of.the.flu + bacterial.pneumonia +
## symptoms.of.the.flu + fever.and.cough + braun.thermoscan +
## how.long.am.i.contagious + home.remedies.for.flu + cough.fever +
## cure.the.flu + low.body.temperature + contagious.flu + headache.cough +
## painful.cough + get.rid.of.flu + normal.body + cough.headache +
## how.to.fight.the.flu + flu.or.cold + over.the.counter.flu.medicine +
## flu.and.fever + viral.bronchitis + thermoscan + taking.temperature +
## influenza.a.and.b + fever.flu + oral.thermometer + the.flu +
## medicine.for.the.flu + treat.a.fever + cough.after.flu +
## acute.bronchitis + what.to.do.when.you.have.the.flu + bronchitis +
## extractum + best.flu.medicine + how.long.are.you.contagious +
## fever.reducers + body.temperature + reduce.fever + flu.remedies +
## anas.barbariae.hepatis.et.cordis + remedies.for.the.flu +
## symptoms.pneumonia + viral.syndrome + the.flu.symptoms +
## what.is.influenza + pneumonia + fever.temperature + child.temperature +
## incubation.period.for.the.flu + high.fever + low.body.temp +
## how.long.does.fever.last + is.it.the.flu + what.to.do.for.the.flu +
## fight.the.flu + symptoms.of.bronchitis + bacterial.bronchitis +
## chest.cough + fever.breaks + cough.and.fever + fever.too.high +
## early.flu.symptoms
##
## Start: AIC=1939.11
## .outcome ~ dangerous.fever + how.long.does.flu.last + i.have.the.flu +
## fever.cough + what.to.eat.when.you.have.the.flu + medicine.for.flu +
## how.long.are.you.contagious.with.the.flu + viral.pneumonia +
## how.to.get.over.the.flu + treat.the.flu + signs.of.the.flu +
## flu.contagious + ear.thermometer + can.dogs.get.the.flu +
## anas.barbariae.hepatis + how.to.treat.flu + cure.flu + treat.flu +
## cold.or.flu + what.is.a.high.fever + oscillococcinum + treatment.for.flu +
## remedies.for.flu + how.to.get.rid.of.the.flu + bacterial.pneumonia +
## symptoms.of.the.flu + fever.and.cough + braun.thermoscan +
## how.long.am.i.contagious + home.remedies.for.flu + cough.fever +
## cure.the.flu + low.body.temperature + contagious.flu + headache.cough +
## painful.cough + get.rid.of.flu + normal.body + cough.headache +
## how.to.fight.the.flu + flu.or.cold + over.the.counter.flu.medicine +
## flu.and.fever + viral.bronchitis + thermoscan + taking.temperature +
## influenza.a.and.b + fever.flu + oral.thermometer + the.flu +
## medicine.for.the.flu + treat.a.fever + cough.after.flu +
## acute.bronchitis + what.to.do.when.you.have.the.flu + bronchitis +
## extractum + best.flu.medicine + how.long.are.you.contagious +
## fever.reducers + body.temperature + reduce.fever + flu.remedies +
## anas.barbariae.hepatis.et.cordis + remedies.for.the.flu +
## symptoms.pneumonia + viral.syndrome + the.flu.symptoms +
## what.is.influenza + pneumonia + fever.temperature + child.temperature +
## incubation.period.for.the.flu + high.fever + low.body.temp +
## how.long.does.fever.last + is.it.the.flu + what.to.do.for.the.flu +
## fight.the.flu + symptoms.of.bronchitis + bacterial.bronchitis +
## chest.cough + fever.breaks + cough.and.fever + fever.too.high +
## early.flu.symptoms
##
## Start: AIC=2159.52
## .outcome ~ dangerous.fever + how.long.does.flu.last + i.have.the.flu +
## fever.cough + what.to.eat.when.you.have.the.flu + medicine.for.flu +
## how.long.are.you.contagious.with.the.flu + viral.pneumonia +
## how.to.get.over.the.flu + treat.the.flu + signs.of.the.flu +
## flu.contagious + ear.thermometer + can.dogs.get.the.flu +
## anas.barbariae.hepatis + how.to.treat.flu + cure.flu + treat.flu +
## cold.or.flu + what.is.a.high.fever + oscillococcinum + treatment.for.flu +
## remedies.for.flu + how.to.get.rid.of.the.flu + bacterial.pneumonia +
## symptoms.of.the.flu + fever.and.cough + braun.thermoscan +
## how.long.am.i.contagious + home.remedies.for.flu + cough.fever +
## cure.the.flu + low.body.temperature + contagious.flu + headache.cough +
## painful.cough + get.rid.of.flu + normal.body + cough.headache +
## how.to.fight.the.flu + flu.or.cold + over.the.counter.flu.medicine +
## flu.and.fever + viral.bronchitis + thermoscan + taking.temperature +
## influenza.a.and.b + fever.flu + oral.thermometer + the.flu +
## medicine.for.the.flu + treat.a.fever + cough.after.flu +
## acute.bronchitis + what.to.do.when.you.have.the.flu + bronchitis +
## extractum + best.flu.medicine + how.long.are.you.contagious +
## fever.reducers + body.temperature + reduce.fever + flu.remedies +
## anas.barbariae.hepatis.et.cordis + remedies.for.the.flu +
## symptoms.pneumonia + viral.syndrome + the.flu.symptoms +
## what.is.influenza + pneumonia + fever.temperature + child.temperature +
## incubation.period.for.the.flu + high.fever + low.body.temp +
## how.long.does.fever.last + is.it.the.flu + what.to.do.for.the.flu +
## fight.the.flu + symptoms.of.bronchitis + bacterial.bronchitis +
## chest.cough + fever.breaks + cough.and.fever + fever.too.high +
## early.flu.symptoms##
## Call:
## lm(formula = .outcome ~ dangerous.fever + how.long.does.flu.last +
## i.have.the.flu + fever.cough + what.to.eat.when.you.have.the.flu +
## medicine.for.flu + how.long.are.you.contagious.with.the.flu +
## viral.pneumonia + how.to.get.over.the.flu + treat.the.flu +
## signs.of.the.flu + flu.contagious + ear.thermometer + can.dogs.get.the.flu +
## anas.barbariae.hepatis + how.to.treat.flu + cure.flu + treat.flu +
## cold.or.flu + what.is.a.high.fever + oscillococcinum + treatment.for.flu +
## remedies.for.flu + how.to.get.rid.of.the.flu + bacterial.pneumonia +
## symptoms.of.the.flu + fever.and.cough + braun.thermoscan +
## how.long.am.i.contagious + home.remedies.for.flu + cough.fever +
## cure.the.flu + low.body.temperature + contagious.flu + headache.cough +
## painful.cough + get.rid.of.flu + normal.body + cough.headache +
## how.to.fight.the.flu + flu.or.cold + over.the.counter.flu.medicine +
## flu.and.fever + viral.bronchitis + thermoscan + taking.temperature +
## influenza.a.and.b + fever.flu + oral.thermometer + the.flu +
## medicine.for.the.flu + treat.a.fever + cough.after.flu +
## acute.bronchitis + what.to.do.when.you.have.the.flu + bronchitis +
## extractum + best.flu.medicine + how.long.are.you.contagious +
## fever.reducers + body.temperature + reduce.fever + flu.remedies +
## anas.barbariae.hepatis.et.cordis + remedies.for.the.flu +
## symptoms.pneumonia + viral.syndrome + the.flu.symptoms +
## what.is.influenza + pneumonia + fever.temperature + child.temperature +
## incubation.period.for.the.flu + high.fever + low.body.temp +
## how.long.does.fever.last + is.it.the.flu + what.to.do.for.the.flu +
## fight.the.flu + symptoms.of.bronchitis + bacterial.bronchitis +
## chest.cough + fever.breaks + cough.and.fever + fever.too.high +
## early.flu.symptoms, data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -727.06 -118.84 13.34 107.51 746.73
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 650.070 102.724 6.328
## dangerous.fever 6.624 44.611 0.148
## how.long.does.flu.last 112.522 113.565 0.991
## i.have.the.flu 47.143 155.974 0.302
## fever.cough 26.160 114.876 0.228
## what.to.eat.when.you.have.the.flu 78.434 90.993 0.862
## medicine.for.flu 73.702 96.988 0.760
## how.long.are.you.contagious.with.the.flu 60.534 94.375 0.641
## viral.pneumonia 131.972 108.066 1.221
## how.to.get.over.the.flu 109.290 88.471 1.235
## treat.the.flu -4.365 143.158 -0.030
## signs.of.the.flu 105.139 136.883 0.768
## flu.contagious -28.723 47.785 -0.601
## ear.thermometer -24.540 46.422 -0.529
## can.dogs.get.the.flu 49.540 88.345 0.561
## anas.barbariae.hepatis 180.924 171.809 1.053
## how.to.treat.flu 54.896 80.958 0.678
## cure.flu 240.281 87.556 2.744
## treat.flu 48.808 61.494 0.794
## cold.or.flu 5.412 78.110 0.069
## what.is.a.high.fever 45.964 89.651 0.513
## oscillococcinum 6.993 41.147 0.170
## treatment.for.flu 118.225 95.295 1.241
## remedies.for.flu -469.385 170.594 -2.751
## how.to.get.rid.of.the.flu 70.409 47.655 1.477
## bacterial.pneumonia -9.192 44.981 -0.204
## symptoms.of.the.flu -146.627 78.035 -1.879
## fever.and.cough -42.277 39.903 -1.060
## braun.thermoscan -30.003 43.484 -0.690
## how.long.am.i.contagious -35.290 100.262 -0.352
## home.remedies.for.flu 75.810 118.393 0.640
## cough.fever -75.190 105.393 -0.713
## cure.the.flu -108.147 100.334 -1.078
## low.body.temperature -164.870 75.767 -2.176
## contagious.flu 74.350 92.466 0.804
## headache.cough 34.856 76.553 0.455
## painful.cough 112.676 88.771 1.269
## get.rid.of.flu 17.503 70.517 0.248
## normal.body -13.401 60.376 -0.222
## cough.headache -19.956 47.638 -0.419
## how.to.fight.the.flu -27.925 71.412 -0.391
## flu.or.cold -224.979 131.513 -1.711
## over.the.counter.flu.medicine -11.040 75.777 -0.146
## flu.and.fever -23.602 63.105 -0.374
## viral.bronchitis -9.749 35.840 -0.272
## thermoscan 35.770 39.797 0.899
## taking.temperature 77.330 46.126 1.676
## influenza.a.and.b 53.689 82.896 0.648
## fever.flu 148.622 121.825 1.220
## oral.thermometer 84.065 75.072 1.120
## the.flu -3.288 26.280 -0.125
## medicine.for.the.flu 38.271 84.036 0.455
## treat.a.fever -83.540 89.522 -0.933
## cough.after.flu -5.898 59.443 -0.099
## acute.bronchitis 48.616 59.122 0.822
## what.to.do.when.you.have.the.flu -46.138 56.425 -0.818
## bronchitis 43.948 68.188 0.645
## extractum -5.358 48.973 -0.109
## best.flu.medicine 13.035 82.488 0.158
## how.long.are.you.contagious -31.320 61.337 -0.511
## fever.reducers 137.137 67.429 2.034
## body.temperature 5.797 45.418 0.128
## reduce.fever -80.360 51.489 -1.561
## flu.remedies -266.712 165.695 -1.610
## anas.barbariae.hepatis.et.cordis -33.038 119.397 -0.277
## remedies.for.the.flu -4.339 104.555 -0.041
## symptoms.pneumonia -36.741 36.220 -1.014
## viral.syndrome 18.963 85.238 0.222
## the.flu.symptoms -8.364 76.729 -0.109
## what.is.influenza 35.666 96.191 0.371
## pneumonia 61.522 48.644 1.265
## fever.temperature 9.903 30.724 0.322
## child.temperature 23.695 67.496 0.351
## incubation.period.for.the.flu -84.795 76.596 -1.107
## high.fever -69.326 63.816 -1.086
## low.body.temp 21.658 39.453 0.549
## how.long.does.fever.last 117.271 83.844 1.399
## is.it.the.flu -17.397 56.482 -0.308
## what.to.do.for.the.flu 4.239 66.492 0.064
## fight.the.flu 148.720 143.110 1.039
## symptoms.of.bronchitis -11.811 123.205 -0.096
## bacterial.bronchitis 15.883 78.877 0.201
## chest.cough -63.952 59.469 -1.075
## fever.breaks -50.428 86.757 -0.581
## cough.and.fever 18.906 40.381 0.468
## fever.too.high 24.154 91.022 0.265
## early.flu.symptoms -48.954 93.830 -0.522
## Pr(>|t|)
## (Intercept) 7.06e-09 ***
## dangerous.fever 0.88225
## how.long.does.flu.last 0.32417
## i.have.the.flu 0.76309
## fever.cough 0.82032
## what.to.eat.when.you.have.the.flu 0.39076
## medicine.for.flu 0.44910
## how.long.are.you.contagious.with.the.flu 0.52272
## viral.pneumonia 0.22487
## how.to.get.over.the.flu 0.21960
## treat.the.flu 0.97574
## signs.of.the.flu 0.44424
## flu.contagious 0.54914
## ear.thermometer 0.59824
## can.dogs.get.the.flu 0.57622
## anas.barbariae.hepatis 0.29485
## how.to.treat.flu 0.49929
## cure.flu 0.00719 **
## treat.flu 0.42925
## cold.or.flu 0.94490
## what.is.a.high.fever 0.60929
## oscillococcinum 0.86540
## treatment.for.flu 0.21765
## remedies.for.flu 0.00704 **
## how.to.get.rid.of.the.flu 0.14269
## bacterial.pneumonia 0.83849
## symptoms.of.the.flu 0.06316 .
## fever.and.cough 0.29192
## braun.thermoscan 0.49181
## how.long.am.i.contagious 0.72560
## home.remedies.for.flu 0.52342
## cough.fever 0.47724
## cure.the.flu 0.28369
## low.body.temperature 0.03191 *
## contagious.flu 0.42326
## headache.cough 0.64987
## painful.cough 0.20729
## get.rid.of.flu 0.80448
## normal.body 0.82480
## cough.headache 0.67619
## how.to.fight.the.flu 0.69660
## flu.or.cold 0.09024 .
## over.the.counter.flu.medicine 0.88445
## flu.and.fever 0.70918
## viral.bronchitis 0.78616
## thermoscan 0.37091
## taking.temperature 0.09677 .
## influenza.a.and.b 0.51868
## fever.flu 0.22535
## oral.thermometer 0.26549
## the.flu 0.90069
## medicine.for.the.flu 0.64980
## treat.a.fever 0.35298
## cough.after.flu 0.92116
## acute.bronchitis 0.41286
## what.to.do.when.you.have.the.flu 0.41547
## bronchitis 0.52072
## extractum 0.91310
## best.flu.medicine 0.87476
## how.long.are.you.contagious 0.61074
## fever.reducers 0.04462 *
## body.temperature 0.89869
## reduce.fever 0.12175
## flu.remedies 0.11063
## anas.barbariae.hepatis.et.cordis 0.78258
## remedies.for.the.flu 0.96698
## symptoms.pneumonia 0.31284
## viral.syndrome 0.82440
## the.flu.symptoms 0.91341
## what.is.influenza 0.71159
## pneumonia 0.20890
## fever.temperature 0.74789
## child.temperature 0.72628
## incubation.period.for.the.flu 0.27093
## high.fever 0.27994
## low.body.temp 0.58427
## how.long.does.fever.last 0.16500
## is.it.the.flu 0.75871
## what.to.do.for.the.flu 0.94929
## fight.the.flu 0.30122
## symptoms.of.bronchitis 0.92382
## bacterial.bronchitis 0.84082
## chest.cough 0.28479
## fever.breaks 0.56238
## cough.and.fever 0.64067
## fever.too.high 0.79128
## early.flu.symptoms 0.60301
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 276.4 on 100 degrees of freedom
## Multiple R-squared: 0.9365, Adjusted R-squared: 0.882
## F-statistic: 17.16 on 86 and 100 DF, p-value: < 2.2e-16
## Loading required package: Matrix## Loading required package: foreach## Loaded glmnet 2.0-18
From the boxplots we can see that the Lasso model performs the best, followed by the small model, then the stepwise, and finally the full model. This implies that there are a few highly important search terms acting as predictors, and most of the dataset is only loosely correlated with cdcflu.
2)
2a)
3)
3a)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.154047e+01 4.347564e-01 -26.544680 2.958355e-155
## X1 2.080898e-05 4.985167e-06 4.174178 2.990638e-05
## X2 5.647103e-03 2.273731e-04 24.836280 3.638120e-136Confidence intervals:
\[ \alpha = 0.05 \\ \hat{\beta}_0 = -11.54, \ \hat{\beta}_0 \ \epsilon \ (-12.39, -10.68) \\ \hat{\beta}_1 = 2.08*10^{-5}, \ \hat{\beta}_1 \ \epsilon \ ( 1.1*10^{-5}, 3.06*10^{-5}) \\ \hat{\beta}_2 = 5.65*10^{-3}, \ \hat{\beta}_2 \ \epsilon \ (5.2*10^{-3}, 6.09*10^{-3}) \]
3b)
\[ \text{Confidence intervals set at the 0.025 and 0.975 percentiles of the distributions.} \\ \hat{\beta}_0 = -11.54, \ \hat{\beta}_0 \ \epsilon \ (-11.54, -11.54) \\ \hat{\beta}_1 = 2.08*10^{-5}, \ \hat{\beta}_1 \ \epsilon \ ( 2.08*10^{-5}, 2.08*10^{-5}) \\ \hat{\beta}_2 = 5.65*10^{-3}, \ \hat{\beta}_2 \ \epsilon \ (5.65*10^{-3}, 5.65*10^{-3}) \]
3c)
\[ \text{The bootstrap method and the standard fitting arrived at the same parameter estimates. The bootstrap method produced tighter} \\ \text{confidence intervals at N=100 without sacraficing performance. Given similar circumstances we generally prefer the standard method} \\ \text{instead of the bootstrap. This is because bootstrap is an approximation of the estimator, while standard model is an approximation} \\ \text{of the true parameter.} \]